Exponential Functions (Graphs)

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What is an exponential function?

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An exponential function is a mathematical function of the form f(x) = a * b^x, where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent.

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What does the graph of an exponential growth function look like?

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The graph of an exponential growth function rises sharply as x increases, starting from a point above the x-axis (if a > 0) and approaching the x-axis but never touching it.

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What does the graph of an exponential decay function look like?

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The graph of an exponential decay function falls sharply as x increases, starting from a point above the x-axis and approaching the x-axis but never touching it.

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What is the y-intercept of an exponential function?

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The y-intercept of an exponential function f(x) = a * b^x is the point (0, a), where 'a' is the initial value of the function.

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How can you identify exponential growth from a graph?

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Exponential growth can be identified by a graph that rises steeply to the right, indicating that the function's value increases rapidly as x increases.

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How can you identify exponential decay from a graph?

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Exponential decay can be identified by a graph that falls steeply to the right, indicating that the function's value decreases rapidly as x increases.

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What is the base in an exponential function?

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The base in an exponential function is the constant 'b' in the function f(x) = a * b^x, which determines the rate of growth or decay.

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What is the difference between linear and exponential functions?

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Linear functions have a constant rate of change, while exponential functions have a variable rate of change that increases or decreases multiplicatively.

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What does it mean if an exponential function has a base less than 1?

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If an exponential function has a base less than 1, it represents exponential decay, meaning the function's value decreases as x increases.

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What does it mean if an exponential function has a base greater than 1?

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If an exponential function has a base greater than 1, it represents exponential growth, meaning the function's value increases as x increases.